PPO (Proximal Policy Optimization) algorithm has demonstrated excellent performance in many fields, and it is considered as a simple version of TRPO (Trust Region Policy Optimization) algorithm. However, the ratio clipping operation in PPO may not always effectively enforce the trust region constraints, this can be a potential factor affecting the stability of the algorithm. In this paper, we propose SPO (Simple Policy Optimization) algorithm, which introduces a novel clipping method for KL divergence between the old and current policies. SPO can effectively enforce the trust region constraints in almost all environments, while still maintaining the simplicity of a first-order algorithm. Comparative experiments in Atari 2600 environments show that SPO sometimes provides stronger performance than PPO. Code is available at https://github.com/MyRepositories-hub/Simple-Policy-Optimization.

Deep Generative Models (DGMs) are versatile tools for learning data representations while adequately incorporating domain knowledge such as the specification of conditional probability distributions. Recently proposed DGMs tackle the important task of comparing data sets from different sources. One such example is the setting of contrastive analysis that focuses on describing patterns that are enriched in a target data set compared to a background data set. The practical deployment of those models often assumes that DGMs naturally infer interpretable and modular latent representations, which is known to be an issue in practice. Consequently, existing methods often rely on ad-hoc regularization schemes, although without any theoretical grounding. Here, we propose a theory of identifiability for comparative DGMs by extending recent advances in the field of non-linear independent component analysis. We show that, while these models lack identifiability across a general class of mixing functions, they surprisingly become identifiable when the mixing function is piece-wise affine (e.g., parameterized by a ReLU neural network). We also investigate the impact of model misspecification, and empirically show that previously proposed regularization techniques for fitting comparative DGMs help with identifiability when the number of latent variables is not known in advance. Finally, we introduce a novel methodology for fitting comparative DGMs that improves the treatment of multiple data sources via multi-objective optimization and that helps adjust the hyperparameter for the regularization in an interpretable manner, using constrained optimization. We empirically validate our theory and new methodology using simulated data as well as a recent data set of genetic perturbations in cells profiled via single-cell RNA sequencing.

Federated learning (FL) enables multiple clients to collaboratively learn a shared model without sharing their individual data. Concerns about utility, privacy, and training efficiency in FL have garnered significant research attention. Differential privacy has emerged as a prevalent technique in FL, safeguarding the privacy of individual user data while impacting utility and training efficiency. Within Differential Privacy Federated Learning (DPFL), previous studies have primarily focused on the utility-privacy trade-off, neglecting training efficiency, which is crucial for timely completion. Moreover, differential privacy achieves privacy by introducing controlled randomness (noise) on selected clients in each communication round. Previous work has mainly examined the impact of noise level ($\sigma$) and communication rounds ($T$) on the privacy-utility dynamic, overlooking other influential factors like the sample ratio ($q$, the proportion of selected clients). This paper systematically formulates an efficiency-constrained utility-privacy bi-objective optimization problem in DPFL, focusing on $\sigma$, $T$, and $q$. We provide a comprehensive theoretical analysis, yielding analytical solutions for the Pareto front. Extensive empirical experiments verify the validity and efficacy of our analysis, offering valuable guidance for low-cost parameter design in DPFL.

Diffusion models for text-to-image (T2I) synthesis, such as Stable Diffusion (SD), have recently demonstrated exceptional capabilities for generating high-quality content. However, this progress has raised several concerns of potential misuse, particularly in creating copyrighted, prohibited, and restricted content, or NSFW (not safe for work) images. While efforts have been made to mitigate such problems, either by implementing a safety filter at the evaluation stage or by fine-tuning models to eliminate undesirable concepts or styles, the effectiveness of these safety measures in dealing with a wide range of prompts remains largely unexplored. In this work, we aim to investigate these safety mechanisms by proposing one novel concept retrieval algorithm for evaluation. We introduce Ring-A-Bell, a model-agnostic red-teaming tool for T2I diffusion models, where the whole evaluation can be prepared in advance without prior knowledge of the target model. Specifically, Ring-A-Bell first performs concept extraction to obtain holistic representations for sensitive and inappropriate concepts. Subsequently, by leveraging the extracted concept, Ring-A-Bell automatically identifies problematic prompts for diffusion models with the corresponding generation of inappropriate content, allowing the user to assess the reliability of deployed safety mechanisms. Finally, we empirically validate our method by testing online services such as Midjourney and various methods of concept removal. Our results show that Ring-A-Bell, by manipulating safe prompting benchmarks, can transform prompts that were originally regarded as safe to evade existing safety mechanisms, thus revealing the defects of the so-called safety mechanisms which could practically lead to the generation of harmful contents.

How to solve high-dimensional linear programs (LPs) efficiently is a fundamental question. Recently, there has been a surge of interest in reducing LP sizes using \textit{random projections}, which can accelerate solving LPs independently of improving LP solvers. In this paper, we explore a new direction of \emph{data-driven projections}, which use projection matrices learned from data instead of random projection matrices. Given data of past $n$-dimensional LPs, we learn an $n\times k$ projection matrix such that $n > k$. When addressing a future LP instance, we reduce its dimensionality from $n$ to $k$ via the learned projection matrix, solve the resulting LP to obtain a $k$-dimensional solution, and apply the learned matrix to it to recover an $n$-dimensional solution. On the theoretical side, a natural question is: how much data is sufficient to ensure the quality of recovered solutions? We address this question based on the framework of \textit{data-driven algorithm design}, which connects the amount of data sufficient for establishing generalization bounds to the \textit{pseudo-dimension} of performance metrics. We obtain an $\tilde{\mathrm{O}}(nk^2)$ upper bound on the pseudo-dimension, where $\tilde{\mathrm{O}}$ compresses logarithmic factors. We also provide an $\Omega(nk)$ lower bound, implying our result is tight up to an $\tilde{\mathrm{O}}(k)$ factor. On the practical side, we explore two natural methods for learning projection matrices: PCA- and gradient-based methods. While the former is simple and efficient, the latter can sometimes lead to better solution quality. Our experiments confirm the practical benefit of learning projection matrices from data, achieving significantly higher solution quality than the existing random projection while greatly reducing the time for solving LPs.

Model predictive control (MPC) has been shown to significantly improve the energy efficiency of buildings while maintaining thermal comfort. Data-driven approaches based on neural networks have been proposed to facilitate system modelling. However, such approaches are generally nonconvex and result in computationally intractable optimization problems. In this work, we design a readily implementable energy management method for small commercial buildings. We then leverage our approach to formulate a real-time demand bidding strategy. We propose a data-driven and mixed-integer convex MPC which is solved via derivative-free optimization given a limited computational time of 5 minutes to respect operational constraints. We consider rooftop unit heating, ventilation, and air conditioning systems with discrete controls to accurately model the operation of most commercial buildings. Our approach uses an input convex recurrent neural network to model the thermal dynamics. We apply our approach in several demand response (DR) settings, including a demand bidding, a time-of-use, and a critical peak rebate program. Controller performance is evaluated on a state-of-the-art building simulation. The proposed approach improves thermal comfort while reducing energy consumption and cost through DR participation, when compared to other data-driven approaches or a set-point controller.

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers, which is commonly used in the optimization literature due to its fast convergence. In contrast to distributed optimization, distributed sampling allows for uncertainty quantification in Bayesian inference tasks. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. For our theoretical results, we use convex optimization tools to establish a fundamental inequality on the generated local sample iterates. This inequality enables us to show convergence of the distribution associated with these iterates to the underlying target distribution in Wasserstein distance. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.

Routes represent an integral part of triggering emotions in drivers. Navigation systems allow users to choose a navigation strategy, such as the fastest or shortest route. However, they do not consider the driver's emotional well-being. We present HappyRouting, a novel navigation-based empathic car interface guiding drivers through real-world traffic while evoking positive emotions. We propose design considerations, derive a technical architecture, and implement a routing optimization framework. Our contribution is a machine learning-based generated emotion map layer, predicting emotions along routes based on static and dynamic contextual data. We evaluated HappyRouting in a real-world driving study (N=13), finding that happy routes increase subjectively perceived valence by 11% (p=.007). Although happy routes take 1.25 times longer on average, participants perceived the happy route as shorter, presenting an emotion-enhanced alternative to today's fastest routing mechanisms. We discuss how emotion-based routing can be integrated into navigation apps, promoting emotional well-being for mobility use.

Distributed allocation finds applications in many scenarios including CPU scheduling, distributed energy resource management, and networked coverage control. In this paper, we propose a fast convergent optimization algorithm with a tunable rate using the signum function. The convergence rate of the proposed algorithm can be managed by changing two parameters. We prove convergence over uniformly-connected multi-agent networks. Therefore, the solution converges even if the network loses connectivity at some finite time intervals. The proposed algorithm is all-time feasible, implying that at any termination time of the algorithm, the resource-demand feasibility holds. This is in contrast to asymptotic feasibility in many dual formulation solutions (e.g., ADMM) that meet resource-demand feasibility over time and asymptotically.

Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However, solving these formulations soon becomes difficult as the network size grows due to the weak linear relaxation and dense constraint matrix. We have seen improvements in recent years with cutting plane algorithms, reformulations, and an heuristic based on Mixed-Integer Linear Programming (MILP). In this work, we propose a more scalable heuristic based on exploring global and local linear relaxations of the neural network model. Our heuristic is competitive with a state-of-the-art MILP solver and the prior heuristic while producing better solutions with increases in input, depth, and number of neurons.